Is there a way I can check if the jets I have in at the moment are the correct ones or anyway to be sure which ones I need to order to match my exhaust?
Yes. The numbers are stamped on the jet itself, and the number corresponds to the orifice hole size. A #100 jet is 1mm diameter. A #98 is 0.98 mm.
The outer carb bowls aren't too hard to remove, and the main jet would just pull out the bottom of the carb body tower. Be aware that both the bowl and the jet have an oring for a seal. And old hard orings seldom reseal. The damaged rubber boot coupler is nearly a certain sign that the carbs have been off the bike, (caused by ham hands and impatience during carb removal). So, it is possible that the jets may not be as Honda delivered, or worse, field modified by a hacker with a drill bit. I recommend that verify the stamping on the jet with a measurement of the orifice. I use the shanks of small drill bits and a measuring device. What you should target is to find #100 jet. I'd check with Check David Silver Spares, were I to live in the UK.
Also is the UNI NU-4055 filter a replacement for the air filter?
Yes. It is a far less expensive option here in California than the $50-$70 stock filter. The UNI is cleanable and reusable for about 10-15 years.
I am going to check the spark plugs today and clean out the air filter and see if that helps at all.
Do check the plugs. My experience and Honda directive says that the paper filter can be "cleaned" once, but replaced yearly. The paper element can never be completely cleaned as new. Looking at the picture you posted, I'd say it is past it's replacement date. If the spark plug tips are black, the choking effect of a past due air filter could be causal (or contributory.).
The carb boot can be replaced by ones available from David Silver Spares in your country.
http://www.davidsilverspares.co.uk/CB550F2-SUPER-SPORT-1977/You should know that the model designator for your bike is F2. And it seems that England versions had their own separate parts list different from the US models. This explains why your headstock number badge is different than US model convention. Ours has the year model in numbers too big to miss.
http://www.cmsnl.com/honda-cb550f2-super-sport-550-four-1977-england_model17121/partslist/Glad to see your available fuel isn't an issue.
Cheers,